O grau topológico de Brouwer e Aplicações.

Abstract

In this work, we study the Brouwer topological degree theory. first, we study some results about analysis in rn, which are important tools on the study of the degree. after that, we associate each triple (f,⌦, y), where ⌦ ⇢ rn,y 2 rn and f a continuous function in ⌦, to a integer number d(f,⌦, y). this function, known as degree, through its properties and consequences, allows us to find meaningful answers about the existence, uniqueness or multiplicity of solutions for the equation f(x) = y. after that, we construct such a function and study some applications of the theory developed. among them, the Brouwer fixed point theorem.